Novel Approaches Characterizing Separation in Fuzzy Topology with Quasi-Coincidence

Abstract

Fuzzy sets were introduced by Zadeh in 1965, and three years later, Chang defined fuzzy topological spaces. Fuzzy topological spaces are families of fuzzy sets that satisfy the three classical axioms of topology. In this paper, we introduce and study some new notions of To separation axioms in fuzzy topological spaces using the quasi-coincident relation for fuzzy sets. Every ordinary (crisp) topological space vacuously satisfies the condition of being quasi-T_o. We define the quasi-separation axioms for fuzzy topological spaces, as quasi-T_o, quasi-T₁, Quasi-T₂. We have introduced and studied some new notions of To separation axioms in fuzzy topological spaces using the quasi-coincident relation for fuzzy sets. These quasi-separation axioms are weaker than the corresponding classical T_o separation axioms, but they are still useful for characterizing and studying fuzzy topological spaces.